A heterogeneous multi-agent system formation control method based on a specified time observer

Abstract

This invention relates to a formation control method for a heterogeneous multi-agent system based on a time-defined observer. The method includes: establishing a dynamic model for each agent in the heterogeneous multi-agent system, treating each agent as a communication node, and constructing a communication topology; collecting state information from neighboring nodes to construct an error system to estimate the leader's state matrix and output matrix; setting an adaptive observer that estimates the convex hull of the leader's state based on the real-time state information of neighboring nodes, combined with the leader's state matrix and output matrix; constructing a time-varying formation tracking control protocol based on the output of the adaptive observer and a time scaling function; initializing the time-varying formation tracking control protocol according to the expected formation structure of the multi-agent system, and updating the state of each agent according to the time-varying formation tracking control protocol through a consensus controller, so that all agents reach a preset formation; this invention can achieve the desired formation shape within a specified time without introducing global information.

Description

Technical Field

[0001] This invention relates to the field of cooperative control of multi-agent systems, and more specifically to a method for formation control of heterogeneous multi-agent systems based on a specified time observer. Background Technology

[0002] In the field of multi-agent systems research, formation control technology has become a widely studied and popular area. A multi-agent system is a system composed of multiple interacting agents, which typically possess perception, computation, and decision-making capabilities, and achieve the system's overall task through communication and cooperation. Multi-agent formation control technology has extremely wide applications in fields such as aviation, autonomous driving, marine monitoring, and the military. Through effective formation control methods, multiple agents can coordinate their movements in space to accomplish complex tasks, such as target tracking, environmental monitoring, and rescue operations.

[0003] Traditional formation control methods are mostly based on the assumption of homogeneous agents, that is, that agents in the system possess the same dynamic model and perception capabilities. However, in practical applications, agents typically exhibit heterogeneity, with differences in dynamic models, motion performance, and observation accuracy among agents. This heterogeneity limits the application of traditional formation control methods in heterogeneous multi-agent systems. Therefore, heterogeneous multi-agent formation control methods have become a research focus in recent years. To address the control challenges posed by heterogeneity, many novel control strategies have been proposed, including leader-follower, cooperative learning, and optimization control methods, to meet the dynamic needs of different agents.

[0004] Furthermore, in practical applications, due to global network topology or task time factors, information between agents may not be transmitted in real time, leading to communication delays or data loss. However, a time-based observer design can achieve the desired observation accuracy within a finite time, enabling the formation control system to achieve effective coordination even without global network topology information. This time-based observer control strategy can improve the robustness and response speed of the formation control system.

[0005] Therefore, designing a novel formation control strategy that combines a time-specified observer method to address the challenges of formation control in heterogeneous multi-agent systems is of significant research importance and practical value. This approach can improve the control accuracy and stability of multi-agent systems under the influence of heterogeneity and uncertainty, thereby promoting the application of multi-agent formation technology in complex environments. Summary of the Invention

[0006] To address the problems existing in the background art, the present invention provides a heterogeneous multi-agent system formation control method based on a specified time observer, comprising the following steps:

[0007] S1: For heterogeneous multi-agent systems, a dynamic model is established for each agent, and each agent is regarded as a communication node to build a communication topology;

[0008] S2: The agent collects the state information of neighboring nodes and constructs the error system to estimate the state matrix and output matrix of the leader;

[0009] S3: Set up an adaptive observer, which estimates the convex hull of the leader's state based on the real-time state information of neighboring nodes, combined with the leader's state matrix and output matrix.

[0010] S4: Based on the output of the adaptive observer, and combined with the time scaling function, a time-varying formation tracking control protocol is constructed.

[0011] S5: Based on the expected formation structure of the multi-agent system, initialize the time-varying formation tracking control protocol, and through the consensus controller, update the state of each agent according to the time-varying formation tracking control protocol so that all agents reach the preset formation.

[0012] The present invention has at least the following beneficial effects:

[0013] This invention proposes a formation control method for heterogeneous multi-agent systems based on a time-specified observer, enabling time-specified tracking of time-varying formations in such systems. The proposed observer does not rely on global network topology information, allowing each agent to estimate the leader's state and system matrix based on neighbor information within a specified time. The formation tracking control protocol dynamically adjusts control parameters through the observer and the introduced time scaling function, unaffected by the system's initial state or the upper limit of settling time, ensuring that the multi-agent system's output converges within a preset time. Attached Figure Description

[0014] Figure 1 This is a flowchart of the method of the present invention;

[0015] Figure 2 This is a formation communication topology diagram according to an embodiment of the present invention;

[0016] Figure 3 This is a diagram showing the observation error of the observer in an embodiment of the present invention.

[0017] Figure 4 This is a diagram showing the output trajectory of each intelligent agent in an embodiment of the present invention;

[0018] Figure 5 The various intelligent agents in this embodiment of the invention output formation tracking error diagrams.

[0019] Figure 6 The diagram shows the formation tracking error under different initial conditions in the embodiments of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The topology of the multi-agent system described in this invention is constrained by the condition that each follower communicates with all leaders or none of the leaders. Even if a follower does not communicate with any leader, it is guaranteed that at least one other follower establishes communication with all leaders and possesses a directed path connecting to that follower.

[0022] Please see Figure 1 This invention provides a method for formation control of heterogeneous multi-agent systems based on a specified time observer, the method including but not limited to the following steps:

[0023] S1: For heterogeneous multi-agent systems, a dynamic model is established for each agent, and each agent is regarded as a communication node to build a communication topology;

[0024] Consider a multi-agent system consisting of M followers and N leaders. The dynamics model of the followers includes:

[0025]

[0026] Where i = 1, 2, ..., M, Represents the state of follower i, n i x represents i The dimension of (t), p represents the output of follower i, and p represents y. i The dimension of (t), u i (t) represents the control input of follower i, A i B i and C i Let B represent a constant matrix with compatible dimensions, and B i It is a full-rank matrix; The state change rate of follower i is represented by t; t represents time t.

[0027] The dynamics of leaders include:

[0028]

[0029] Where k = M+1, M+2, ..., M+N, Represents the state of leader k, n i x represents k The dimension of (t); p represents the output of leader k, and p represents y. k The dimension of (t) is S and R, which represent the leader's state matrix and output matrix, respectively, and have a compatibility dimension.

[0030] Set up a communication topology that meets certain specific conditions, such as Figure 2 As shown, each follower communicates with all leaders or none of them. Even if a follower does not communicate with any leader, it is guaranteed that at least one other follower communicates with all leaders and has a directed path connecting to all of those followers. Figure 2 Numbers 7, 8, and 9 represent leaders, while numbers 1 through 6 represent followers.

[0031] S2: The agent collects the state information of neighboring nodes and constructs the error system to estimate the state matrix and output matrix of the leader;

[0032] Since the relative information of the leader cannot be directly shared with all followers, an observer was established to obtain the leader's state information using the relative information of its neighbors. The following is a real-time observation of the leader system matrix:

[0033] S21: Construct an error system based on the state information of neighboring nodes collected by the agent:

[0034]

[0035] Where α and γ represent positive parameters selected by the user, and T s T represents the estimated time for matrix S; R Represents the estimated time for matrix R; μ() represents the time scaling function; I represents the derivative of the time scaling function; q Represents a q-order identity matrix; T denotes matrix transpose; S represents the state matrix estimation error of leader i. i The matrix represents the estimation of the leader's state matrix by agent i; R represents the output matrix estimation error of leader i. i This represents the estimated matrix of agent i's output matrix to the leader; Representation matrix The rate of change; Representation matrix The rate of change; This represents the Kronecker product operation;

[0036] S22: Estimate the leader's state matrix and output matrix based on the constructed error system:

[0037]

[0038] Among them, S j R represents the estimation matrix of agent j of the leader's state matrix. j This represents the estimated matrix of agent j for the leader's output matrix; Representation matrix S i The rate of change; Represents matrix R i The rate of change.

[0039] S3: Set up an adaptive observer, which estimates the convex hull of the leader's state based on the real-time state information of neighboring nodes, combined with the leader's state matrix and output matrix.

[0040] The adaptive observer includes:

[0041]

[0042] in, ξ represents the observation error between agent i and agent j; i ν represents the estimate of the convex hull of the leader state by agent i. i For coupling gain, ν i0 α is the initial value of the coupling gain, and γ are positive parameters selected by the user; T1 represents the observation time preset by the adaptive observer; T represents the transpose.

[0043] It is clear from the expression of the adaptive observer that the time scaling function μ(t,T) u This plays a crucial role in accelerating the convergence speed. However, when hour, The observation time tending towards infinity indicates that the observer is using a high gain. In this case, even slight disturbances can have a significant impact on the system. To address this issue, choosing an observation time that is longer than the actual engineering time is a simple and effective solution.

[0044] Preferably, the time scaling function includes:

[0045]

[0046]

[0047] Where s>0 represents a parameter greater than 0, T u This indicates the preset time selected by the user.

[0048] S4: Based on the output of the adaptive observer, and combined with the time scaling function, a time-varying formation tracking control protocol is constructed.

[0049] Preferably, the time-varying formation tracking control protocol of the heterogeneous multi-agent system includes:

[0050]

[0051] Where K 1i Satisfy A i +B i K 1i It is a hurwitz matrix, and K 2i (t)=Ψ i (t)-K 1i Φ i (t), K 3i (t)=K 2i (t)+K 4i (t). To ensure that the required formation is completed within the specified time, when t∈(0,T) max ), T max =max{T S ,T R}, by calculating using Lemma 1, we can obtain (Φ i (t),Ψ i (t)). Lemma 1 is defined as follows: for any initial state If ∈>0 is large enough, the following system

[0052]

[0053] There exists a unique bounded solution, and

[0054]

[0055] in express The rate of change; vec() represents the operation of converting a matrix into a vector. This represents the corresponding inverse operation; q represents the dimension of the leader state; n i The dimension representing the follower state; m i This indicates the dimension of the follower's input;

[0056] When t∈[T] max When (, +∞), directly solving the regulator equation yields (Φ i ,Ψ i );

[0057]

[0058] K 4i (t) is a solution to the following equation:

[0059]

[0060] Where A i B i C i S is a known constant matrix with compatible dimensions, and S and R are the system matrices of the leader. i Let K be the estimated matrix of S. i This is the transition matrix.

[0061] S5: Based on the expected formation structure of the multi-agent system, initialize the time-varying formation tracking control protocol, and through the consensus controller, update the state of each agent according to the time-varying formation tracking control protocol so that all agents reach the preset formation.

[0062] Preferably, the time-varying formation tracking control protocol includes:

[0063]

[0064] Among them, K 1i Satisfy A i +B i K 1i The hurwitz matrix, x i ξ represents the state of agent i. i φ represents the output of the adaptive observer. i This represents the offset of agent i relative to the leader, and For n i An identity matrix of order 1. Representation matrix B i The Moore-Penrose pseudo-inverse matrix, K 2i (t)=Ψ i (t)-K 1i Φ i (t) represents the observer gain matrix, K 3i (t)=K 2i (t)+K 4i (t) represents the formation gain matrix, (Ψ) i ,Φ i K represents the solution of the regulator. 4i (t) represents the formation compensation amount, K i It is the transition matrix, and T2 represents the user-preset formation convergence time.

[0065] Preferably, all agents reach a preset formation when the following conditions are met:

[0066]

[0067] Among them, y i (t) represents the output of agent i at the current time, φ yi (t) is the desired output offset of the formation, β k (k = M+1, M+2, ..., M+N) satisfies Let N be the convex hulls of the N leaders.

[0068] The expected formation is composed of time-varying vectors in It is piecewise continuously differentiable. The corresponding output formation offset is φ. yi (t)=Rφ i (t).

[0069] N agents cooperate to achieve and maintain a desired formation. Formation in a multi-agent system refers to a group of agents that can satisfy certain geometric constraints or shapes. In this invention, formation is described based on the relative position vectors between agents. A time-varying vector φ is set. i Let (t) represent the desired state formation of each agent. This vector changes over time, indicating the characteristics of time-varying formations.

[0070] Furthermore, the condition for achieving a consistent formation is that, over time, the error between the convex hull of the agent's state and the leader's state, as well as the error of the expected formation, eventually reaches zero, that is:

[0071]

[0072] This embodiment considers a heterogeneous multi-agent system consisting of nine agents, where the follower subset... and the subset of leaders The dynamics of followers 1, 3, and 5 are: The dynamics of followers 2, 4, and 6 are: The dynamics of leaders 7, 8, and 9 are: In addition, the expected formation structure was designed:

[0073]

[0074] Where i = 1, 2, ..., 6.

[0075] To verify the effectiveness of the proposed time-varying formation based on a specified time observer, simulation verification was performed using MATLAB. This embodiment uses... Figure 2 For the experimental topology, the six follower agents will eventually form a regular hexagon. Regarding the parameter values ​​in the system, we choose s = 3, α = 3, γ = 2, ∈ = 15, and the respective parameter matrices. Randomly select the agent's initial position state x1(0) = [1,1] T x2(0) = [-1, 1, 0] T x3(0) = [0,1] T x4(0) = [1,2,1] T x5(0) = [3,0] T x6(0) = [1, -1, -1] T x7(0) = [0,1,0,1] T x8(0) = [1,1,0,1] T x9(0) = [0,1,1,1] T They move in the 2D plane;

[0076] Select T S =T R =1s, T1=2s, T2=5s. From the simulation results, it can be concluded that, Figure 3 As shown, it represents the error between the observed value and the actual leader convex hull. We can see that an accurate estimate can be obtained within T1. Figure 4 The output trajectory snapshots at different times within t=30s are shown, indicating that before T2, the followers had formed a rotating hexagon around the leader's center. Figure 5 This also indicates that the output tracking error of each agent had become zero before T2, further demonstrating the successful achievement of the expected formation. Furthermore, Figure 6 The results show the tracking error variation under different initial states, highlighting the advantage of our method in maintaining convergence speed while adapting to the initial state.

[0077] Simulation experiments have verified that, based on the novel adaptive time-specified observer and control protocol, stable tracking of the formation within a preset time period can be achieved through neighbor interactions without relying on global network topology information. Compared with existing control methods, the proposed method features time controllability, distributed implementation, and adaptability to unknown system matrices, thus overcoming the shortcomings of current technologies in complex system applications.

[0078] It should be noted that those skilled in the art will understand that all or part of the processes in the above method embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0079] The above description is merely a specific embodiment of this application. It should be noted that those skilled in the art will understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for formation control of heterogeneous multi-agent systems based on a specified-time observer, characterized in that, Includes the following steps: S1: For heterogeneous multi-agent systems, a dynamic model is established for each agent, and each agent is regarded as a communication node to build a communication topology; S2: The agent collects the state information of neighboring nodes and constructs the error system to estimate the state matrix and output matrix of the leader; S3: Set up an adaptive observer, which estimates the convex hull of the leader's state based on the real-time state information of neighboring nodes, combined with the leader's state matrix and output matrix. The adaptive observer includes: in, Represents intelligent agents and intelligent agents The observation error between them; Represents intelligent agents The estimated value of the convex hull of the leader's state. For coupling gain, This is the initial value of the coupling gain. These are positive parameters selected by the user. This indicates the pre-set observation time for the adaptive observer; Indicates transpose; Represents intelligent agents An estimation matrix for the leader's state matrix; Indicates the time scaling function; express Time; S4: Based on the output of the adaptive observer and combined with the time scaling function, a time-varying formation tracking control protocol is constructed; The time scaling function includes: in, This represents a parameter that is greater than 0. This indicates the preset time selected by the user; The time-varying formation tracking and control protocol includes: in, satisfy The hurwitz matrix, Represents intelligent agents state, This represents the output of the adaptive observer. Represents intelligent agents Compared to the leader's offset, and , for An identity matrix of order 1. Representation matrix Moore-Penrose pseudo-inverse matrix, Represents the observer gain matrix. Represents the formation gain matrix. This represents the solution for the regulator. For formation compensation amount, It is a transition matrix. This indicates the user-preset formation convergence time; S5: Based on the expected formation structure of the multi-agent system, initialize the time-varying formation tracking control protocol, and through the consensus controller, update the state of each agent according to the time-varying formation tracking control protocol so that all agents reach the preset formation.

2. The heterogeneous multi-agent system formation control method based on a specified time observer according to claim 1, characterized in that, The process of constructing a communication topology includes: Constructing a directed graph ,Include One follower and One leader, among whom Represents a set of nodes. Represents an edge set. It is a picture The adjacency matrix, Represents communication node To communication node The edge weights, where if and only if hour ,otherwise ;node Neighborhood collection It is indicated that the Laplace matrix is ​​defined as follows: ,in , ; Let represent a diagonal matrix function; assuming all leaders have no neighbors, then ,in, express The Laplace matrix of the subgraph formed by the number of follower nodes Indicates from Each follower node to The Laplace matrix portion determined by the connection relationships of the leader nodes.

3. The heterogeneous multi-agent system formation control method based on a specified time observer according to claim 2, characterized in that, The dynamic model of the intelligent agent is a heterogeneous multi-agent system, including... One follower and There are 1 leader; among them, the dynamics model of followers includes: in, , Indicates follower state, express Dimensions Indicates follower The output, express Dimensions Indicates follower The control input, , and Let represent a constant matrix with compatible dimensions, and It is a full-rank matrix; Indicates follower The rate of change of state; express time; The dynamics of leaders include: in, , Indicates the leader state, express The dimension; Indicates the leader The output, express Dimensions and These represent the leader's state matrix and output matrix, respectively, and have a compatibility dimension.

4. The heterogeneous multi-agent system formation control method based on a specified time observer according to claim 3, wherein step S2 includes: S21: Construct an error system based on the state information of neighboring nodes collected by the agent: in, and This represents the positive parameter selected by the user. Representation matrix Estimated time; Representation matrix Estimated time; Indicates the time scaling function; This represents the derivative of the time scaling function; express An identity matrix of order 1; , Indicates matrix transpose; Indicates the leader The state matrix estimation error, Represents intelligent agents An estimation matrix for the leader's state matrix; Indicates the leader The output matrix estimation error, Represents intelligent agents An estimated matrix for the leader's output matrix; Representation matrix The rate of change; Representation matrix The rate of change; This represents the Kronecker product operation; S22: Estimate the leader's state matrix and output matrix based on the constructed error system: in, Represents intelligent agents The estimation matrix of the leader's state matrix. Represents intelligent agents An estimated matrix for the leader's output matrix; Representation matrix The rate of change; Representation matrix The rate of change.

5. The heterogeneous multi-agent system formation control method based on a specified time observer according to claim 4, characterized in that, All agents will form a pre-defined formation when the following conditions are met: in, For the intelligent agent at the current moment The output, It is the expected output offset of the formation. satisfy , express The convex hull of a leader.

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